so if a player multiclasses into two classes that grant the player a fighting style and they choose archery on both classes does that stack. I have looked in the players handbook and did not see a conflict here. this would essentially give them a +4 to ranged attacks. can anyone find a rule that clarifies this?

Under fighter, ranger and paladin fighting style description it says:

You can’t take a Fighting Style option more than once, even if you later get to choose again.

So you can’t take it twice.

Technically they should not be allowed to take the same fighting style more than once, but DDB’s system isn’t sophisticated enough to prevent that yet.